Question

can figure n be rotated and then translated to form figure n?
no
how can figure n be translated and then reflected to form figure n?
complete the statement.
figure n is translated 5 units up,
then reflected across the x-axis.

Explanation:

First Question: Can figure \( N \) be rotated and then translated to form figure \( N'' \)?

To determine if a rotation followed by a translation can map \( N \) to \( N'' \), we analyze the orientation and shape. Rotation changes the orientation (angle) of the figure, while translation moves it without rotating. By visually inspecting (or analyzing the grid), the orientation of \( N \) and \( N'' \) doesn't match a rotation - translation sequence (since rotation would alter the angle, but here the required transformation is more likely reflection - translation or other, but for rotation - translation, the key is if rotation can align it to then translate. Since the answer is given as "no", we confirm:

Step1: Analyze rotation - translation possibility

Rotation changes the figure's angle, translation moves it. The figures' orientation doesn't allow rotation then translation to match \( N'' \). So the answer is no.

Second Question: How can figure \( N \) be translated and then reflected to form figure \( N'' \)?

Step1: Determine translation direction

Looking at the grid (and the given dropdown with "up" as an option), translating 5 units up moves \( N \) vertically to align for reflection.

Step2: Determine reflection axis

Reflecting across the \( x \) - axis (as per the dropdown) flips the figure over the \( x \) - axis, which, after the upward translation, maps \( N \) to \( N'' \).

Answer:

s:

1. For "Can figure \( N \) be rotated and then translated to form figure \( N'' \)?": no
2. For "How can figure \( N \) be translated and then reflected to form figure \( N'' \)?": Figure \( N \) is translated 5 units up, then reflected across the \( x \) - axis.